Final Answer:
Dijkstra's algorithm is designed to find the shortest path from a start node to every other node in a graph, making the statement ""True."" It operates on weighted graphs, ensuring optimality in finding paths with the minimum sum of weights (option a).
Step-by-step explanation:
Dijkstra's algorithm is indeed designed to determine the shortest path from a start node to every other node in a graph. The algorithm, named after computer scientist Edsger W. Dijkstra, uses a greedy approach to iteratively explore and update the distances to neighboring nodes, ultimately providing the shortest paths. The key idea is to maintain a priority queue of nodes, consistently selecting the one with the smallest tentative distance for exploration. This process continues until the shortest paths to all nodes are determined (option a).
Dijkstra's algorithm operates on weighted graphs, where each edge has an associated numerical value or weight. The algorithm ensures that the distances calculated represent the minimum sum of weights along the paths. It guarantees optimality as long as the weights are non-negative, making it particularly useful in various applications, such as network routing and road mapping. The efficiency of Dijkstra's algorithm lies in its ability to make locally optimal choices at each step, leading to a globally optimal solution for finding the shortest paths in a graph.
In conclusion, the statement that Dijkstra's algorithm can determine the distance from a start node to every node in the graph is true. Its widespread use in network optimization and routing attests to its effectiveness in solving real-world problems where finding the shortest paths is crucial.